This application claims priority from Japanese Application No. JP 10-316248 filed Nov. 6, 1998, the entire content of which is hereby incorporated by reference.
1. Field of the Invention
The present invention relates to a crystal section shape measuring method which optically measures the sectional shape of a single crystal pulled by the Czochralski method (CZ method).
2. Description of the Related Art
The CZ method is one of the methods for producing single crystal as the raw material for a semiconductor. In the CZ method, as shown in FIG. 7, a crucible 2 provided in a furnace body 1 of the CZ furnace is filled with a crystal melt liquid 3, from which the single crystal 4 is pulled by a pulling apparatus 5 while being rotated by a rotating apparatus 6. Upward motion of the crucible 2 is controlled in such a way that the heating center of a heater 7 keeps a constant relative position with the liquid level, in order to evenly heat the crystal melt liquid 3 by the heater 7.
It is preferable that the single crystal 4 takes a target shape at its upper and lower ends while being pulled. It is also preferable that the crystal body and seed crystal have a uniform diameter equal to the target value during the same process. Moreover, it is preferable to keep its deformation factor [(maximum diameter -minimum diameter)/minimum diameter], representing distortion from the roundness of the sectional shape of the single crystal 4, at an allowable level.
As for the product quality, it is preferable to control the density of oxidation-induced stacking faults (hereinafter referred to as OSF) to a low level. OSF, as one of the crystal evaluation criteria, is a stacking fault caused by the phenomenon wherein oxygen, dissolved in the crystal to form a solid solution, separates out as an oxide while the crystal is thermally treated for oxidation. The OSF density decreases as pulling speed increases because of the accelerated quenching of the crystal. It is therefore preferable to increase the pulling speed. This also advantageously increases production efficiency.
However, increasing the pulling speed increases the deformation factor, possibly beyond the allowable limit, thus decreasing product yield. It is therefore preferable to set the optimum pulling speed at which the crystal is pulled while keeping the deformation factor within an allowable range, for improved single crystal yield and production efficiency and securing product quality. It is therefore important to accurately measure the sectional shape of the single crystal while it is pulled and thereby to accurately determine its deformation factor.
The known methods for measuring the sectional shape of the single crystal being pulled by the CZ method falls into two general categories. One is the weight method, which tries to determine the crystal diameter from its weight, and the other is the optical method, which tries to determine the crystal diameter using an optical apparatus, such as a CCD camera.
Pulling the crystal by the CZ method, however, is accompanied by the formation of projections 4a, referred to as crystal habit lines, regularly formed in the peripheral direction on the outer peripheral face of the single crystal 4, as shown in FIG. 9. The projections 4a extend in the crystallographic axis direction, and are formed at peripheral positions characteristic of the crystal orientation of the single crystal 4. In order to accurately determine the deformation factor of the crystal, it is preferable to measure the shape of the crystal habit portions.
The weight method, which tries to determine the crystal diameter from the weight and length of the single crystal pulled, covers only the average diameter and is incapable of measuring the detailed sectional shape involving the crystal habit lines. The optical method, on the other hand, measures the shape more accurately than the weight method, because it reads the diameter of the fusion ring high in brilliance, formed at the interface between the crystal melt liquid and the single crystal, as the diameter of the crystal.
The optical method, as shown in FIG. 7, takes an image (measures light) of the base of the single crystal 4 by an optical apparatus, e.g., a one-dimensional CCD camera 8, set at an upper oblique position over the crystal 4, through a window 9 provided at the top of the furnace body 1. The points C and C, at which the fusion ring A formed around the base of the single crystal 4 intersects the light measuring line Bxe2x80x94B, are located from the brilliance change at these points C and C, in order to measure sectional shape of the crystal 4, as shown in FIG. 8.
More precisely, the intersection points C and C are continuously located, while the single crystal 4 makes one rotation, to find the interval W(xcex1) between the points C and C by the following equation:
W(xcex1)=L(xcex1)xe2x88x92R(xcex1)
wherein,
L(xcex1) and R(xcex1) are the detected positions of the intersection points C and C, and xcex1 is the angle of rotation of the single crystal. The diameter across the entire periphery of the single crystal 4 is thus measured.
However, when the one-dimensional CCD camera 8 is set in such a way that its light measuring line Bxe2x80x94B passes through the crystal center O, the fusion ring A will stand in the single crystal 4""s light when the diameter of the crystal diminishes, causing a measuring error and perhaps making the measurement impossible.
In the actual pulling process, therefore, the one-dimensional CCD camera 8 is set in such a way as to take a photograph (measures light) of the crystal center O of the single crystal 4""s base on the side of the camera. As a result, the light measuring line Bxe2x80x94B intersects the fusion ring A on the camera side from the crystal center O. In this case, the crystal diameter is determined by the following equation from the interval W between the intersection points C and C, measured by the one-dimensional CCD camera 8:
D=(W2+4r2)xc2xd
wherein,
D is the crystal diameter,
W is the interval between intersection points C and C, and
r is the distance from the crystal center O to the light measuring line Bxe2x80x94B.
However, when the one-dimensional CCD camera 8 is set in such a way as to have the light measuring line Bxe2x80x94B on the camera side (this side) from the crystal center O, two crystal habit lines 4a and 4a, opposite each other about the crystal center O, cannot pass the light measuring line Bxe2x80x94B simultaneously, the one following the other to pass the line. Therefore, accuracy of diameter measurement decreases significantly, when the diameter is measured in the vicinity of the crystal habit line 4a by the conventional optical method, which tries to determine the distance W between the intersection points C and C from the difference between the detected C positions L(xcex1) and R(xcex1).
Furthermore, none of the presently known methods can accurately sense the liquid level for controlling upward motion of the crucible, which means that the measured liquid level invariably involves an error. As a result, the light measuring line Bxe2x80x94B of the one-dimensional CCD camera 8 will deviate from the initially set position, causing the distance (r) between the crystal center O and the light measuring line Bxe2x80x94B to change. The measured diameter D therefore. involves an error.
In order to solve these problems, Japanese Patent Laid-open No. 63-256594 discloses a method which moves the light measuring line Bxe2x80x94B of the. one-dimensional CCD camera 8 in the direction perpendicular to the line, trying to find the true diameter from the crystal diameters determined before and after the movement and from the distance of the movement. However, even this method cannot avoid the decreased accuracy of the diameter measurement in the vicinity of the crystal habit line, because the light measuring line is apart from the crystal center.
Under these circumstances, the inventors of the present invention have proposed (Japanese Patent Laid-Open No. 9-100194) a method for measuring the crystal diameter, comprising of steps: (1) separately detecting the two points, positions L(xcex1) and R(xcex1), at which the fusion ring A and light measuring line Bxe2x80x94B intersect each other on each side; (2) finding a timing lag xcex8 for detecting the positional changes of these points, determined by the camera""s measuring line position; and (3) comparing these positions L(xcex1) and R(xcex1) with each other after removing the timing lag xcex8, to prevent decreased accuracy of the diameter measured in the vicinity of the crystal habit line, caused by the light measuring line Bxe2x80x94B being apart from the crystal center O.
The single crystal pulled by the CZ method has the crystal habit lines in the peripheral direction on the outer peripheral face of the crystal at positions characteristic of the crystal orientation, as mentioned earlier. For example, the crystal habit lines appear at intervals of 90xc2x0 for the crystal orientation (100). The single crystal is rotated in the peripheral direction while it is being pulled, and the intersection points of the fusion ring A and light measuring line Bxe2x80x94B of the one-dimensional CCD camera change in their positions when the line crosses the crystal habit line. For the crystal orientation of (100), the intersecting position changes at intervals of 90xc2x0.
The positional changes of the intersection points occur simultaneously on both sides when the light measuring line Bxe2x80x94B passes the crystal center O, but there is a timing lag of these positional changes as the line Bxe2x80x94B leaves the crystal center O, the lag xcex8 becoming larger as the distance (r) between the crystal center O and line Bxe2x80x94B increases.
The inventors of the present invention have developed (Japanese Patent Application Laid-Open No. 9-100194) a crystal diameter measuring method with which the decreased accuracy of the diameter measured in the vicinity of the crystal habit line, resulting from the light measuring line Bxe2x80x94B being apart from the crystal center O, can be prevented. This is achieved by comparing the positions L(xcex1) and R(xcex1) of O, the intersection points on both sides, with each other after removing the timing lag xcex8 of positional changes of these points from the detected positions L(xcex1) and R(xcex1).
The inventors of the present invention have also developed another crystal diameter measuring method (Japanese Patent Laid-Open No. 9-40151), which can prevent not only the decreased accuracy of the diameter measured in the vicinity of the crystal habit line resulting from the light measuring line Bxe2x80x94B being apart from the crystal center O, but also the decreased accuracy of the measured diameter resulting from shaking motion of the crystal.
The single crystal being pulled by the CZ method is shaken at a frequency of 1 to 4 oscillations for every one rotation. When the single crystal is shaken in the lateral direction, viewed from the optical appliance, the effect of shaking can be removed by finding the difference between the positions L(xcex1) and R(xcex1), to solve the shaking-caused problems. When it is shaken back and forth, on the other hand, the accuracy of the diameter measurement decreases as a result of the changed distance between the light measuring line Bxe2x80x94B and the crystal center O. However, the single crystal is shaken in a complex manner when it is actually pulled, which is a major cause for the decreased accuracy of diameter measurement, even when the detected positions L(xcex1) and R(xcex1) are compared with each other to remove the effect of the timing lag xcex8 for detecting the positional changes of intersection points.
In view if this problem, the inventors of the present invention have developed (Japanese Patent Application No. 9-40151) yet another crystal diameter measuring method with which the accuracy of the diameter measurement can be further improved by removing the component due to the shaking motion of the single crystal from the detected positional data of the intersection points on both sides, because it removes not only the measurement error resulting from the timing lag for detecting the positional changes of these points caused by the crystal habit line, but also the effect of the shaking motion of the single crystal. One of the useful methods for removing the component due to the shaking motion of the single crystal from the detected positional data of the intersection points on both sides is the Fast Fourier Transform (FFT), applied to the detected positional data to find their frequency components, and removes the frequency component of the lower order, corresponding to the shaking period of the single crystal, from each of the frequency components found.
The response, speed of the optical apparatus used to detect the intersection point positions on both sides is essential. It is preferable, as indicated by the results of analysis of crystal section shapes, that the measurement pitch is 2xc2x0 or less in terms of the angle of rotation of the single crystal, in order to accurately measure the crystal section shape in the vicinity of the crystal habit line. It is therefore preferable in a diameter measuring method to secure a response time of the optical apparatus in such a way that it works at a measurement pitch of 2xc2x0 or less.
A one-dimensional CCD camera as the optical apparatus can cope with high speed pulling because it is now developed to work at a relatively high speed. However, it is preferable to accurately position the crystal center and set the light measuring line, in order to accurately determine the diameter of the crystal. This requires the one-dimensional CCD camera to be set at a varying position in such a way as to follow the changed crystal center position, needing many additional steps. It is possible to automatically set the light measuring line by mechanical scanning, at an additional cost. These problems can be solved by the use of a two-dimensional CCD camera.
An ordinary two-dimensional CCD camera works at a response speed of 30 frames/s. However, the high-speed pulling needs a high-speed camera, which is much more expensive than an ordinary one. It should also be noted that a two-dimensional CCD camera generally has a smaller number of camera picture elements in the horizontal direction, and hence tends to be lower in accuracy of the measured crystal section shape than a one-dimensional CCD camera. It is difficult for a two-dimensional CCD camera, having an increased number of camera picture elements for improved resolution, to also satisfy the response time requirement.
Therefore, there is a need for a method which uses a two-dimensional CCD camera to measure the diameter of a crystal being pulled at a high speed and at a measurement pitch of 2xc2x0 or less.
It is an object of the present invention to provide a high-precision, economical crystal section shape measuring method, which uses a two-dimensional CCD camera to measure the crystal diameter at a measurement pitch of 2xc2x0 or less even when the crystal is pulled at a high speed.
In order to attain the above object, the crystal section measuring method of the present invention comprises steps of: (1) taking an image with a two-dimensional CCD camera of the base of a single crystal on the side of the camera, the single crystal being pulled by the CZ method from a crystal melt liquid while rotating, the two-dimensional CCD camera being set at an upper oblique position over the single crystal, in the horizontal and vertical directions; (2) setting in the image taken by the two-dimensional CCD camera, two or more horizontal light measuring lines, arranged in parallel to each other in the vertical direction; (3) separately detecting the intersection positions, i.e. the points on both sides at which the fusion ring intersects the light measuring line on each light measuring line; (4) combining the pair of the intersection points obtained on each light measuring line to interpolate the space between the measurement pitches, determined by the camera""s response speed and the crystal rotational speed; and (5) comparing the detected positions of the intersection points on both sides with each other, subsequent to the interpolation for the space between pitches, after removing the timing lag for detecting the positional changes of these points, in order to measure the distance between the intersection points on each light measuring line and thereby to determine the single crystal section shape.
Thus, the method of the present invention allows to measure the distance between the intersection points on both sides, at a pitch smaller than that determined by the camera""s response speed and crystal rotational speed.
It is preferable, in order to improve the measurement accuracy for the crystal section measuring method of the present invention, to remove the effect of the shaking motion of the single crystal by separately processing a pair of the intersection points on each light measuring line by FFT, and estimating the component due to the shaking motion of the crystal which is to be subtracted from the detected positional data of the intersection points on each light measuring line.
It is also preferable to automatically set two or more horizontal light measuring lines in the image taken by the two-dimensional CCD camera in accordance with the camera""s response speed and crystal rotational speed, in order to improve the operation of the present invention.
For finding the crystal center position, a simple and preferable procedure is to scan the horizontal light measuring lines in the vertical direction in the image taken by the two-dimensional CCD camera during the seed drawing process, and find the midpoint between the intersection points on the horizontal plane on which the distance between the intersection points with the fusion ring around the seed crystal becomes the largest.